一种求解激波问题的中心差分-WENO混合方法研究

Investigation of a Hybrid Central Difference-WENO

关键词:  中心差分格式  WENO格式  混合方法  低耗散  激波诱导燃烧

Key words:  Central difference scheme  WENO scheme  Hybrid method  Low dissipation  Shock-induced combustion

摘要:

为提高求解包含激波问题的计算精度和效率，发展了一种低耗散、高效率的中心差分-WENO(Weighted Essentially Non-Oscillatory)混合格式，Navier-Stokes方程的无黏项在光滑流场区域采用六阶中心差分格式离散，而间断附近采用五阶WENO格式求解；基于密度设计了一种新型格式开关实现两种格式在光滑区域和间断之间自动切换，确保数值解在间断附近基本无振荡。针对一维激波熵波作用问题验证了混合格式的低耗散特性；对二维Riemann问题的研究表明发展的基于密度的格式开关更为合理，混合格式的计算效率较WENO格式明显提高；将其应用到激波诱导燃烧问题中，混合格式能很好地捕捉定常流场中激波和化学反应锋面的位置以及非定常流场的振荡频率。

Abstract:

In order to improve the accuracy and efficiency solving the flowfield with shocks，a low dissipation，high efficiency and hybrid central difference-WENO method is developed. The inviscid flux of Navier-Stokes equations is discretized by sixth-order central difference scheme in smooth field，but near the discontinuity fifth-order WENO scheme is adopted. Based on density a new scheme switch is developed to achieve the switchover of these two schemes between smooth zone and discontinuity，and make sure that there is no oscillatory near the discontinuity. The test of one-dimensional shock and entropy wave interaction is used to validate the low dissipation of hybrid scheme. The test of two-dimensional Riemann shows that the scheme switch based on density is more appropriate and the efficiency is improved obviously compared with WENO scheme. Applying high order hybrid scheme to shock-induced combustion shows that it can capture the shock，reaction front in steady flow and oscillatory frequency in unsteady flow.